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30 July 2011

Framing appropriate questions for conceptual physics

I've been working a bit with my colleagues on our 9th grade conceptual physics course.  We teach a rigorous physics (not "physical science") class to all 9th graders.  It's a difficult proposition to aim the material at the correct level.  Many students have not taken algebra, and those who have are certainly not fluent in algebra skills.*  We want to minimize arithmetic, and concentrate on conceptual skills.

* Those top-15% students who are fluent in algebra are broken out into a section of Honors Physics I.

Nevertheless, we want to teach serious physics, not merely a set of facts to be learned or situations to be memorized.  We still teach physical reasoning from equations, for example... but in the sense of "mass doesn't change, speed doubles, so by ½mv2 , kinetic energy quadruples."  This is some of the same fundamental understanding expected from AP-level students, but at a slower pace, with fewer equations, and without a calculator necessary.

Problem is, it's tough to find questions at this appropriate level.  Hewitt's conceptual physics text is a great source, of course, but I'm talking about finding a huge bank of questions that will allow you to write numerous quizzes, tests, and exams.  For college-level physics, the AP program provides more questions than you'll ever need.  At the general but quantitative level, the New York Regents exam is the way to go.  I have not yet found a good non-quantitative, published source of questions that are ready to copy-and-paste into your tests.

Now, the Regents exam includes occasional qualitative questions.  These can be used nearly verbatim in conceptual physics.  Most of the Regents questions include arithmetic or algebra, though, often emphasizing the mathematics through the phrase, "show all work, including the equation and substitution with units."  I have no complaints about this quantitative approach; in fact, I train my junior-level general class to handle Regents-style questions.  I just know from our department's experience that, for freshmen, "substitution with units" presents a considerable barrier to physics understanding.

Try turning a quantitative Regents question into a no-calculator conceptual physics question.  For example, from the January 2006 exam:

The speed of a wagon increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly down a hill.  What is the magnitude of the acceleration of the wagon during this 3.0-second interval?
(1) 0.83 m/s2     (2) 2.2 m/s2      (3) 3.0 m/s2       (4) 3.8 m/s2

Four different ideas occur:

Ask about the acceleration's direction instead of its magnitude.  Freshmen can learn the fundamental fact that speeding up means acceleration and velocity are in the same direction, while slowing down means acceleration and velocity are in opposite directions.  I'd write...

A wagon travels down a hill.  The wagon's speed increases from 2.5 m/s to 9.0 m/s in 3.0 s.  What is the direction of the wagon's acceleration?
(A) up the hill       (B) down the hill   
(C) straight down     (D) straight up

Ask for a straightforward calculation of the acceleration.  Even though I'm making the problems accessible without a calculator, I'm not ignoring quantitave reasoning entirely.  It *is* important that a student recognize that acceleration depends on the change in an object's velocity, not on the velocity itself.  So, I'd write...

The speed of a wagon increases from 9 m/s to 12 m/s in 3 s as it accelerates uniformly down a hill. What is the magnitude of the acceleration of the wagon during this 3.0-second interval?
(1) 1 m/s2     (2) 3 m/s2      (3) 3.5 m/s2       (4) 4 m/s2

Trying to just divide any old velocity by 3 s leads to an incorrect answer.  The the correct answer can be determined at a glance, even by a mathematically inept ninth grader.  (Math teachers will cheer now, because we're forcing students not to grab a calculator to manipulate (12-9)/3.)

Ask for a comparison to familiar values.  The only acceleration that our students probably have a feel for is g.  So, ask...

The speed of a wagon increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly down a hill.  Is the magnitude of this wagon's acceleration...
(A) greater than Earth's free-fall acceleration
(B) less than Earth's free-fall acceleration
(C) equal to Earth's free-fall acceleration

Such a question does NOT necessarily require a direct calculation of the wagon's acceleration.  If the student thinks in Hewitt-ese, then speeding up in free-fall means gaining 10 m/s of speed every second of fall.  This wagon accelerated for 3 s, and gained nowhere near 30 m/s of speed, giving (B) as the only possible answer.

Ask about the physical meaning of numbers.  Even without calculators, our students should develop a feel for the physical reality represented by numerical answers.  Speeds in m/s can be estimated in mph by multiplying by 2 and adding a bit.  But I'm not asking anything truly quantitative here:

The speed of an object increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly.  Which of the following objects could NOT reasonably perform this motion?
(A) A car on an interstate  
(B) An airplane during takeoff  
(C) A lab cart on a track in the classroom
(D) A bicyclist going down a hill

There you have it -- FOUR different conceptual physics multiple choice items inspired by a single Regents question.  And any one of these questions can be expanded into an open-response test item,  or assigned for homework, by adding the phrase, "justify your answer."  

1 comment:

  1. Loved this. I'm in the middle of creating question banks for the upcoming year to pull from as I make skilled based exams and this is exactly what I needed, thanks!